The core idea of MCDropout is to enable dropout regularization at both training and test time. With multiple forward passes at inference time, the prediction is not deterministic and can be used to estimate the posterior distribution. As a result, MCDropout offers Bayesian interpretation. First proposed in [1]}, the authors established the theoretical framework of
MCDropout as approximate Bayesian inference and proved MCDropout minimises the Kullback–Leibler divergence
between an approximate distribution and the posterior of
a deep Gaussian process. More formally, let \(d_l\)  denotes dropout at the \(l\) -th layer of a neural network, where \(d_l \sim Bernoulli(p)\) . Then at inference time, with \(K\)  forward passes, we obtained a distribution of \(K\)  logits and predictions per test data, where we can compute the expected value, standard deviation, variation ratio and entropy to assess uncertainty.
